Jens Niegemann, Inst. f. Feldtheorie/Höchstfreq, ETH Zürich, Switzerland
Time-integration for discontinuous Galerkin tiime-domain simulations of Maxwell's equations
25 Mars 2014, 10h30, salle Galois Coriolis

The discontinuous Galerkin (DG) approach has gained considerable attention as an efficient and accurate method for solving Maxwell's equations in time-domain. Its ability to allow explicit time integration while offering a higher-order spatial discretization on unstructured meshes makes it a very attractive method for complex electromagnetic systems [1]. In order to match the accurate spatial discretization one typically also requires an efficient higher-order time integration method. In practice, explicit low-storage Runge-Kutta (LSRK) schemes were shown to offer an excellent compromise of accuracy, performance and memory consumption. Here, we will present several new low-storage Runge-Kutta methods which significantly improve both the efficiency and the accuracy of DG time-domain simulations of Maxwell's equations. First, we present novel LSRK schemes in the 2N formulation with up to 22 stages. Besides optimized schemes of 4th order [2], we also discuss new methods of 5th order. In addition, we also demonstrate embedded Runge-Kutta pairs in the low-storage 3S* formulation [3] with optimized stability contours for both the main and the embedded schemes. Using the embedded scheme for error estimation then allows us to automatically adapt the timestep in large scale DG calculations. Finally, we will also briefly discuss some recent progress in the development of local timestepping.

[1] K. Busch, M. K\"onig, J. Niegemann, "Discontinuous Galerkin methods in nanophotonics", Laser & Photonics Reviews 5, 773-809 (2011) [2] J. Niegemann, R. Diehl, K. Busch, "Efficient low-storage Runge–Kutta schemes with optimized stability regions", J. Comput. Phys. 231, 364-372 (2012) [3] D. Ketcheson, "Runge-Kutta methods with minimum storage implementations", J. Comput. Phys. 229, 1763-1773 (2010)

Gabriel Barrenechea, Department of Mathematics and Statistics, University of Strathclyde, Glasgow, Scotland, United Kingdom
Some recent results on algebraic flux correction schemes

2 Avril 2014, 10h30, salle Galois Coriolis

The numerical approximation of the convection-diffusion equation is known to be challenging, especially in the convection-dominated regime. One of the main drawbacks is the lack of positivity preserving schemes, i.e., schemes that satisfy the discrete maximum principle. Moreover, a classical result states that a linear scheme preserving the maximum principle can only be of first order. Then, an alternative approach has been to introduce nonlinear schemes, mostly inspired by the idea of shock capturing, to solve this equation.

One scheme that has received some attention over the last few years is the algebraic-flux correction scheme. The origins of this method can be traced back to the late eighties, but they have been reframed recently in the works by D. Kuzmin. In this talk I will review some recent analytical results for this scheme, showing its advantages and limitations, and showing a modification of it that makes it possible to prove that the discrete problem has a solution. Some preliminary numerical results are also presented. This work has been carried out in collaboration with Volker John (WIAS, Berlin), and Petr Knobloch (Charles University, Prague).

PDF of the presentation

Daniel Le Roux, Institut Camille Jourdan, Université Claude Bernard, Lyon 1
Discrete analyses and numerical simulation of typical waves for environmental problems
8 Avril 2014, 14h00, salle Galois Coriolis

The shallow-water system, obtained from the Navier-Stokes equations by vertical averaging, is extensively used in environmental studies (ocean, atmosphere, rivers) to simulate the propagation of a number of typical waves (e.g. gravity, Rossby). For most of the discretization schemes, the numerical approximation of shallow-water models is a delicate problem leading to the appearance of noisy and spurious solutions in the representation of the waves. In order to understand these difficulties and to select appropriate spatial discretization schemes, Fourier / dispersion analyses and the study of the null space of the associated discretized problems have proven beneficial. The aim of this talk is to present such results and to propose a class of possible discretization schemes, that is not affected by the spurious solutions.

Thierry Dumont, Institut Camille Jourdan, Université Claude Bernard, Lyon 1
Vers une implantation efficace de méthodes multi-résolution ?
8 Avril 2014, 15h00, salle Galois Coriolis

Les méthodes multi-résolution sont attrayantes quant il s’agit de résoudre des problèmes dont la solution peut-être représentée de manière parcimonieuse, par exemple pour approcher les ondes des systèmes de réaction-diffusion. Malheureusement, leur implantation est complexe et délicate. Je décrirai d’abord sommairement ces méthodes et leur application à la Réaction–Diffusion. L’essentiel de l’exposé portera sur une implantation parallèle en mémoire partagée et sur les performances obtenues. Le parallélisme est implémenté par des techniques de vol de tâches, en utilisant la bibliothèque Intel Tbb dont je décrirai l’utilisation.

Ivan Voznyuk, Institut Fresnel, HIPE )Hyperfrequency, Instrumentation, Processing, Experimentation) team, Marseille
FETI–DPEM2–full method as an efficient technic applied to 3D electromagnetic large-scale simulation
27 Mai 2014, 14h00, salle Galois Coriolis

The Finite-element method (FEM) is well suited for solving problems involving inhomogeneous and arbitrary shaped objects. Unfortunately, the modeling and analysis with FEM is technically very challenging because of the requirement time and memory, especially for the large-scale 3D electromagnetic computations.

At the present time, the domain-decomposition method (DDM) is one of the most efficient and versatile algorithms involving parallel computations. Related FETI (Finite Element Tearing and Interconnecting) method also seems very robust when one is dealing with arbitrary mesh partitions. Recently, we proposed an extension of the FETI-DPEM2 method[1], named as FETI-DPEM2-full method, where we imposed a Robin type boundary conditions at each interface point. Three-dimensional configurations were considered as well [2].

In this talk I will review recent results obtained for

    1/ The large-scale 3D direct Electromagnetic scattering problems
    2/ The 3D Inverse scattering applications

[1] I. Voznyuk, H. Tortel and A. Litman, PIER, 139, 247–263, 2013
[2] I. Voznyuk, H. Tortel and A. Litman, submitted to IEEE TAP, 2014

PDF of the presentation

Axel Modave, Applied Mechanics and Mathematics (MEMA) Université catholique de Louvain, Belgium
Perfectly matched layers for wave-like time-dependent problems – Design, discretization and optimization
3 Juin 2014, 10h30, salle Galois Coriolis

The numerical simulation of wave propagation problems set in very large or infinite spatial domains is a major challenge. A classical strategy consists in considering only a limited computational domain with an artificial boundary that requires a specific treatment. The perfectly matched layer (PML) technique, introduced twenty years ago, provides an efficient way to deal with such artificial boundary, and is now used for a wide range of problems. However, the extension of PML formulations to more and more complicated cases is difficult and some issues remain, especially for time-dependent problems. In this talk, three key topics are treated. First, the choice of PML parameters is analyzed in discrete contexts, with the aim of optimizing the PML effectiveness. Then, a procedure to design PML formulations for generally shaped computational domains is explained. It permits a great flexibility when choosing the shape of the domain. Finally, alternative PML formulations are discussed and compared from different aspects (well-posedness, stability, computational efficiency, …). Numerical results, mainly based on discontinuous Galerkin finite element schemes, are presented along this talk.

PDF of the presentation

Christopher Harder, Mathematical and Computer Sciences, Metropolitan State University of Denver, Mathematical and Computer Sciences, USA
The MHM framework
18 Juin 2014, 14h30, salle Lagrange Gris

Hybrid formulations of partial differential equations in a domain are naturally reduced to differential equations defined on a triangulation of the domain. The Multiscale Hybrid-Mixed framework is built upon hybrid formulations with a threefold set of goals: 1) a divide-and-conquer strategy to split much of the problem into completely independent subproblems; 2) the formulation of variables associated with mixed versions of the original problem; and 3) the development of finite element methods with well-understood convergence properties and highly localized a posteriori estimators. The finite element methods developed in this framework are often (but not always) two-level methods, which adds a layer complexity to the analysis. We will develop the framework and understand its numerical properties. Examples will be pulled from the classical Laplace, advection-reaction-diffusion, and elasticity problems.

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Rodolfo Araya, Departamento de Ingeniería Matemática, Facultad de Ciencias Físicas y Matemáticas, Universidad de Concepción, Chile
An adaptive RELP method applied to two CFD problems
2 juillet 2014, 15h30, salle Coriolis

In this talk we will present and analyze an adaptive residual local projection finite element method, for two important equations: Advection-diffusion and Navier-Stokes. In both cases we are interested in to develop an stabilized approach to improve the quality of the computed solution with a small computational effort.

PDF of the presentation

Antoine Moreau, Institut Pascal, Université Blaise Pascal
Nanophotonique et plasmonique
15 Juillet 2013, 14h00, salle Galois Coriolis

PDF of the presentation

Nicolas Bonod, Institut Fresnel, Marseille
Augmenter l'interaction lumière-matière à des échelles sub-longueur d'onde avec des résonateurs photoniques
28 juillet 2014, 10h30, salle Coriolis

Au cours de ce séminaire, j'introduirai la notion de résonance électromagnétique et montrerai comment des particules de taille inférieure à la longueur d'onde peuvent interagir de manière résonante avec le champ électromagnétique. Ces résonateurs photoniques trouvent des applications importantes aussi bien dans le contrôle de l'émission spontanée et la conception de sources compactes de lumière que dans l'imagerie médicale par résonance magnétique (IRM).

Alexandra Christophe, LGEP, Paris
Méthode des éléments finis avec joints en recouvrement non-conforme de maillages: application à la simulation magnétodynamique
29 octoibre 2014, 10h30, salle Byron blanc

Notre étude vise à développer et à évaluer une méthode de décomposition de domaine avec recouvrement dans le cadre de la modélisation du contrôle non destructif (CND) par courants de Foucault (CF). L'objectif d'une telle approche consiste à éviter le re- maillage systématique de l'intégralité du domaine d'étude lors du déplacement de l'un de ses éléments constitutifs (par exemple, déplacement de la sonde CF au dessus de la pièce contrôlée). Plus précisement, il s'agit de concevoir une méthode de décomposition de domaine avec recouvrement qui s'appuie sur la théorie apportée par la méthode des éléments finis avec joints. En plus de s'affranchir de la contrainte d'une interface d'échange invariante avec le mouvement, la technique décrite dans ce travail réalise des transferts d'information réciproques entre les domaines. Dans cet exposé, on présente les résultats théoriques ainsi que numériques liés à la simulation magnétodynamique. Par ailleurs, l'intérêt d'une telle méthode est illustré par des applications sur des cofigurations bidimensionnelles de CND par CF.

Thomas Toulorge, Université catholique de Louvain, Institute of Mechanics, Materials and Civil Engineering
High-order mesh generation: validity, numerical properties and geometrical approximation
11 décembre 2014, 10h30, salle Coriolis

In the computational physics community, a consensus is forming on the superior efficiency of high-order numerical schemes for problems with high resolution requirements. However, many contributions show that linear geometrical discretizations can limit the accuracy of high-order methods. The need for curvilinear mesh generation tools is becoming acute as high-order schemes, such as Discontinuous Galerkin methods, are becoming mature enough for practical applications.

In this talk, we will address specific issues raised by high-order mesh generation. We will first focus on the problem of robustly assessing and enforcing the validity of the mesh. We will then consider the implications of the curvilinear nature of the mesh on the numerical scheme, in terms of stability and accuracy. Finally, we will show how the representation of the exact geometrical model by the boundaries of the high-order mesh can be improved. The methods presented in this talk are publicly available through the free software package Gmsh.

C2S@Exa Inria Project Lab

HOSCAR CNPa-Inria project

Software suite for computational nanophotonics/nanoplasmonics

Seminars in 2015


Toward petaflop numerical simulation on parallel hybrid architectures, June 6-10, 2011, INRIA Sophia Antipolis-Méditerranée, France

Conferences in 2011

3rd International Conference on Finite Element Methods in Engineering and Science (FEMTEC 2011), May 9 - 13, 2011, Harvey's Casino and Resort South Lake Tahoe, USA

Postdoctoral project
Numerical modeling of the interaction of an electromagnetic field with living tissues using a discontinuous finite element method
Application deadline: March 15th

PhD project
Modélisation de la variabilité entre les individus dans le calcul électromagnétique des effets de la téléphonie mobile

Internship and PhD\\ Schémas d'intégration en temps précis et efficaces pour les équations de Maxwell discrétisées par une méthode d'éléments finis discontinus d'ordre élevé

Sujets de stages 2010 Schémas numériques performants pour la propagation d'ondes électromagnétique Méthode éléments finis hybride pour la propagation d'ondes électromagnétiques

ONERA scientific event

High accuracy numerical methods and their application to complex physics problems, December 7-8 2009, ONERA Toulouse, France

Conferences in 2010

2nd European Seminar on Coupled Problems (ESCO 2010), June 28—July 2, 2010, Pilsen, Czech Republic


Robust methods and algorithms for solving large algebraic systems on modern high performance computing systems, March 30-April 3 2009, INRIA Sophia Antipolis-Méditerranée, France
Slides of the lectures

Scientific activity reports

2007 to 2013

>>clip<< Seminars in 2008

Siham Layouni, CEA Saclay
April 21st 2008

Jan S. Hesthaven, Brown University, Division of Applied Mathematics
July 21st 2008

Martin J. Gander, Geneva University, Mathematics Section
August 18th 2008

Oliver Rheinbach, Universitaet Duisburg-Essen, Fachbereich Mathematik
December 2nd 2008

>>clip<< Seminars in 2007

Martin J. Gander
July 9th 2007

Sarah Delcourte
November 13th 2007

José Carcione
November 26th 2007

Numerical modeling of wave propagation in elastic media
December 11th 2007